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Sagot :
Answer:
P = 4L - 10
A = [tex]\rm L^2-5L[/tex]
Step-by-step explanation:
Area & Perimeter
Area
By taking the product of a 2-D shape's side lengths, the area calculates how much space a 2-D shape takes up.
Perimeter
A 2-D shape's perimeter is the sum of all its side lengths.
[tex]\hrulefill[/tex]
Solving the Problem
Width
We're told that the width is 5 less than the length.
If the measurement of the width is W, and the measurement of the length is L inches then,
W = L - 5.
Perimeter
The side lengths of a rectangle are 2 with a measurement of the width and 2 with length.
So,
P = L + L + W + W or 2(L + W)
P = 2[L + (L - 5)} = 2(2L - 5)
P = 4L - 10
Area
The area of a rectangle is the product of its width and length.
So,
A = LW = L(L - 5) = [tex]\rm L^2-5L[/tex].
The perimeter of the rectangle can be written as a function of the length p(l)= 4l - 10. The area of the rectangle can be written as a function of the length a(l)= [tex]\underline{l^2 - 5l}[/tex].
Let l represent the length of the rectangle.
Since the width is 5 inches shorter than the length, let w = l - 5.
Perimeter Function
- The perimeter P of a rectangle is given by the formula:
[tex]P = 2l + 2w[/tex]
- Substituting w:
[tex]P(l) = 2l + 2(l - 5)[/tex]
- Simplifying this:
[tex]P(l) = 2l + 2l - 10 = 4l - 10[/tex]
Area Function:
- The area A of a rectangle is given by the formula:
[tex]A=l\cdot w[/tex]
- Substituting w:
[tex]A(l) = l \cdot (l - 5)[/tex]
- Simplifying this:
[tex]A(l) = l^2 - 5l[/tex].
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